With 37 saves and his fifth win of the campaign, John Gibson played in his 448th game as a Duck, passing Guy Hebert for the most by a goaltender in franchise history.
Carlsson tucked the shootout winner on his first career attempt, beating Avs goaltender Ivan Prosvetov with a silky head-fake and move to the forehand.
Bowen Byram scored twice for the Avalanche, who fell to 15-6-2 on the season. Devon Toews also scored. Prosvetov made 34 saves.
Both teams would have great scoring chances in the opening minute of the game, but it would be Colorado taking the night's first lead on a wrister from the slot by Byram. Just seconds after Prosvetov denied Leason on the breakaway with a left pad stop, Byram converted a setup feed from Ross Colton on the other end, beating Gibson through the five-hole.
With two goals on the night, Byram now has eight points in 24 games this season. He totalled career-highs in goals (10), assists (14), points (24) and games played (42) last year.
Byram added to the lead a few minutes later, lifting a snapshot over Gibson's shoulder on an odd-man rush.
With the secondary assist, Colorado defenseman Josh Manson recorded his first point against his original NHL team.
Byram's two first-period markers secured his second career NHL multi-goal performance.
Anaheim temporarily got back within two late in the first on Henrique's power-play goal, a backdoor tap-in after a terrific cross-ice pass by Strome down low.